The meaning of residence time

The solutions to Eqs. (2A2.1) and (2A2.7). (A) The volume of water, V, in the pool as a function of time Vpoo is the final value when the pool is full. (B) The relative concentration, C, of coli in the pool as a function of time. Cj is the concentration in the inflow and Co is the concentration at time t = 0. Residence times, r, are indicated for both models. 

We define the residence time, Tflu, as the time when the pool starts overflowing, as illustrated in Fig. 2A2.1 

In this analogy the residence time is the time at which the volume of the system reaches steady state (i.e. the volume at overflow). 

Now let s make the analogy a little more realistic. The pool is full, but the water has gotten dirty. It has E. coli bacteria of concentration C (molm ), and you want to renew the water in the pool rvith clean water that has an E. coli concentration of At t = 0 you begin the 

Since the concentration of E. coli in the pool as5miptotically approaches that of the inflowing water, the pool water wdl theoretically never be totally renewed, so one defines a time, Trenew. when a certain fraction of the old water has been replaced. What is the time Trenew. and how much water has been replaced at this time  

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Concluding, the axial diffusion and nonuniform flow in FAIMS gaps (i) reduce the mean of residence times tjes by 30%, which increases sensitivity and decreases resolution of planar FAIMS and (ii) spread around the mean with hardly any effect on those metrics. The latter applies to operation at fixed or slow-changing Ec but not when Eq varies so fast that A c during compares with the peak widths in FAIMS spectra, in which case the width of distribution is important (4.3.11). Defining the physical limitations on E scan speed is cmcial to acceleration of FAIMS analyses that is topical to many existing and prospective applications. 

Several reactors deviate from the ideal flow patterns presented in the previous chapters. This is why it is important to understand the meaning of residence time distribution (RTD) in the system under consideration. In this chapter, a basic characterization of RTDs will be presented. It is relevant, however, to emphasize that in studies of purely physical systems, such as different kinds of mixing chambers, knowledge of the RTD of the system can be considerably beneficial. Before the actual, detailed treatment of the problem, we will briefly define the concepts of residence time and RTDs. 

In aerobic processes, the mean sludge residence time is typically 5 to 10 days. The hydraulic residence time is typically 0.2 to 0.3 days. Suspended growth aerobic processes are capable of removing up to 95 percent of BOD. 

Fig. 12. The relationship between the mean oceanic residence time, T, yr, and the seawater—cmstal rock partition ratio,, of the elements adapted from Ref. 29. , Pretransition metals I, transition metals , B-metals , nonmetals. Open symbols indicate T-values estimated from sedimentation rates. The sohd line indicates the linear regression fit, and the dashed curves show the Working-Hotelling confidence band at the 0.1% significance level. The horizontal broken line indicates the time required for one stirring revolution of the ocean, T. ...

Now, the ratio of the mean phase residence times is the time the solute spends in the mobile phase divided by the time spent in the stationary phase. Thus,... 

A fines removal system is installed on the crystallizer designed in the first example. Assuming that the cut size for the fines removal system is 50 im and the ratio of mean residence times for product and fines, rp/rp( = 7), is 10, calculate the mean product residence time now required to produce the same dominant size of 600 pm at the same production rate and suspension density. 

Chemically reactive elements should have a short residence time in seawater and a low concentration. A positive correlation exists between the mean ocean residence time and the mean oceanic concentration however, the scatter is too great for the plot to be used for predictive purposes. Whitfield and Turner (1979) and Whitfield (1979) have shown that a more important correlation exists between residence time and a measure of the partitioning of the elements between the ocean and crustal rocks. The rationale behind this approach is that the oceanic concentrations have been roughly constant, while the elements in crustal rocks have cycled through the oceans. This partitioning of the elements may reflect the long-term chemical controls. The relationship can be summarized by an equation of the form... 

Fig. 6 Comparison of results of the AF model solved with and without streamflow trend for wet and dry years, expressed as years above and below the mean water residence time in the reservoir (0.25 years)...

The characterization is performed by means of residence time distribution (RTD) investigation [23]. Typically, holdup is low, and therefore the mean residence time is expected to be relatively short Consequently, it is required to shorten the distance between the pulse injection and the reactor inlet. Besides, it is necessary to use specific experimental techniques with fast time response. Since it is rather difficult, in practice, to perfectly perform a Dirac pulse, a signal deconvolution between inlet and outlet signals is always required. 

Li, Y.-H. (1982). A brief discussion on the mean oceanic residence time of elements. 

One measure of activated sludge systems is the mean cell residence time or sludge age. The different types of systems and much of US terminology is involved with Sludge Age. 

Table II gives the residence time of C02 in the atmosphere before entering the sea as estimated from various data. The results of several different approaches to the data of Figure 1 (Column 4) suggest that the mean atmospheric residence time of C02 before entering the mixed layer of the sea is around 4 to 5 years, in good agreement with some of the earlier estimates based on natural 14C. A residence time of 10 years or more, which has sometimes been advocated, now seems to be untenable.

Slurry condition 1 density, 1.33 g/cm3 viscosity, 89 mPa- s Slurry condition 2 density, 1.20 g/cm3 viscosity, 3.2 mPa - s From the slurry introduction point, bitumen droplets must rise a distance of 0.80 m within the mean vessel residence time of 45 min in order to reach the froth layer and be recovered. What kind of oil recovery efficiencies would be predicted for each case ... 

The NPD is given by Eq. 9.2-44 (which is equivalent to Eq. El 1.3-3) where X = tft is given in Eq. 9.2-47, and it is the ratio of residence time in the extruder (given by the ratio of free volume of the screw to SSE volumetric flow rate, V/Q) to the mean circulation time over the flight zone (given by the ratio of the free volume of the screw to the total (drag) flow rate... 

A well-known traditional approach adopted in chemical engineering to circumvent the intrinsic difficulties in obtaining the complete velocity distribution map is the characterization of nonideal flow patterns by means of residence time distribution (RTD) experiments where typically the response of apiece of process equipment is measured due to a disturbance of the inlet concentration of a tracer. From the measured response of the system (i.e., the concentration of the tracer measured in the outlet stream of the relevant piece of process equipment) the differential residence time distribution E(t) can be obtained where E(t)dt represents... 

The idealized plug-flow and bateh reactors are the only two classes of reaetors in which all the atoms in the reaetors have the same residenee time. In all other reactor types, the various atoms in the feed spend different times inside the reactor that is, there is a distribution of residenee times of the material within the reactor. For example, eonsider the CSTR the feed introduced into a CSTR at any given time beeomes eompletely mixed with the material already in the reactor. In other words, some of the atoms entering the CSTR leave it almost immediately, because material is being continuously withdrawn from the reactor other atoms remain in the reactor almost forever because all the material is never removed from the reactor at one time. Many of the atoms, of eourse, leave the reactor after spending a period of time somewhere in the vieinity of the mean residence time. In any reactor, the distribution of residence times ean significantly affect its performance. 

The second moment about the mean is a measme of the spread of the distribution about the mean. The variance of residence times in a perfectly mixed tank reactor is (let x = tlx)... 

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